For a science fair competition, a group of high school students build a kicker-m

Q: For a science fair competition, a group of high school students build a kicker-m

(a) along vertical initial velocity, voy = vo*sintheta acceleration ay = -g afrter falling on the ground total displacement y = 0 from equation of motion y = voy*T + 0.5*ay*T^2 0 = v*sintheta*T - 0.5*g*T^2 T = 2*v*sintheta/g along horizantal initial speed vox = v*costheta acceleration ax = 0 time = T from equation of motion x = vox*t + 0.5*ax*t^2 X = v*costheta*2*v*sintheta/g + 0 X = v^2*sin(2theta)/g X = 39.5^2*sin(2*33.6)/9.8 X = 146.8 m

ID: 1456457 • Letter: F

Question

For a science fair competition, a group of high school students build a kicker-machine that can launch a golf ball from the origin with a velocity of 39.5 m/s and initial angle of 33.6°with respect to the horizontal.

(a) Where will the golf ball fall back to the ground?

(b) How high will it be at the highest point of its trajectory?

(c) What is the ball's velocity vector (in Cartesian components) at the highest point of its trajectory?

= m/s

(d) What is the ball's acceleration vector (in Cartesian components) at the highest point of its trajectory?

= m/s2

Explanation / Answer

(a)

along vertical

initial velocity, voy = vo*sintheta

acceleration ay = -g

afrter falling on the ground

total displacement y = 0

from equation of motion

y = voy*T + 0.5*ay*T^2

0 = v*sintheta*T - 0.5*g*T^2

T = 2*v*sintheta/g

along horizantal

initial speed vox = v*costheta

acceleration ax = 0

time = T

from equation of motion x = vox*t + 0.5*ax*t^2

X = v*costheta*2*v*sintheta/g + 0

X = v^2*sin(2theta)/g

X = 39.5^2*sin(2*33.6)/9.8

X = 146.8 m <<<<-------answer

H = (voy^2)/2g

H = (39.5*sin33.6)^2/(2*9.8)

H = 24.4 m

(c)

v = vox i = 39.5*cos33.6i = 32.9 i

(d)

a = -9.8j